Question: Simplify the following expression: $ n = \dfrac{-7z - 5}{2} - \dfrac{-1}{2} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{2}{2}$ $ \dfrac{-7z - 5}{2} \times \dfrac{2}{2} = \dfrac{-14z - 10}{4} $ Multiply the second expression by $\dfrac{2}{2}$ $ \dfrac{-1}{2} \times \dfrac{2}{2} = \dfrac{-2}{4} $ Therefore $ n = \dfrac{-14z - 10}{4} - \dfrac{-2}{4} $ Now the expressions have the same denominator we can simply subtract the numerators: $n = \dfrac{-14z - 10 + 2 }{4} $ Distribute the negative sign: $n = \dfrac{-14z - 10 + 2}{4}$ $n = \dfrac{-14z - 8}{4}$ Simplify the expression by dividing the numerator and denominator by 2: $n = \dfrac{-7z - 4}{2}$